How can you prove that the orbits of the planets are flat and that the planes of the orbits retain their position in space?

Kepler’s second law follows from the law of conservation of angular momentum in the Sun – planet system, which asserts the constancy of the planet’s sector velocity vector. This means that the orbit of any planet is flat and that the position of the plane of the planet’s orbit remains unchanged in space. The influence of the nonspherical shape of the planet, the effect of other planets can be neglected.